1. Field of the Invention
The present invention relates to a stage driving system, and more particularly to a stage driving system for moving a movable stage, supporting an article to be worked or exposed or a specimen, positioning the same at a target position, adapted for use in an exposure apparatus or a working apparatus employed for producing a semiconductor device, an image pickup device, a display device, a magnetic head or the like, or in an observing apparatus such as an electron microscope.
2. Related Background Art
In the electron microscope employing an electron beam or in the exposure apparatus for semiconductor device manufacture such as a stepper, there is employed a configuration in which a positioning device for the specimen or the work piece is loaded on an antivibration device. The positioning device is usually composed of an X-Y stage which is driven in two horizontal directions. The antivibration device has a function of attenuating the vibrations by vibration absorbing means, such as an air spring, a coil spring, antivibration rubber etc. However, such an antivibration device can attenuate, to a certain extent, the vibrations transmitted from the floor, but is incapable of effectively attenuating the vibrations generated by the positioning device itself loaded on the antivibration device. More specifically, the reaction generated by the high-speed movement of the positioning device itself causes a vibration in the antivibration device, thereby hindering the high-speed and high-precision positioning of the positioning device.
For example, FIG. 1 shows an error signal in a position control system when a positioning device (movable stage) loaded on a base plate equipped with an antivibration device is step driven. As shown in FIG. 1, in the initial stage, there appears a transient vibration of the natural frequency of the position control system. This vibration however attenuates relatively quickly, and the vibration of the natural frequency of the base plate overlaps the subsequent signal for a long period, thus prolonging the time required for positioning.
This phenomenon can be quantified by a dynamic model of the movable stage loaded on the base plate in the following manner.
FIG. 2 shows a dynamic model of an X-Y stage 1 loaded on a base plate 2, represented to travel in a horizontal axis such as the X- or Y-direction. The dynamic model has two degrees of freedom, including the base plate 2 and the stage 1. The equations of motion of the stage can be represented in the following manner, utilizing the symbols shown in FIG. 1: EQU m.sub.1 x.sub.1 +b.sub.1 (x.sub.1 -x.sub.2)+k.sub.1 (x.sub.1 -x.sub.2)=f.sub.1 ( 1a) EQU m.sub.2 x.sub.2 +b.sub.2 x.sub.2 +k.sub.2 x.sub.2 +b.sub.1 (x.sub.2 -x.sub.1)+k.sub.1 (x.sub.2 -x.sub.1)=-f.sub.1 ( 1b)
where the symbols used therein have the following meanings:
m.sub.1 : mass of stage kg! PA1 m.sub.2 : mass of base plate kg! PA1 b.sub.1 : viscous friction coefficient of stage Ns/m! PA1 b.sub.2 : viscous friction coefficient of base plate Ns/m! PA1 k.sub.1 : spring constant of stage N/m! PA1 k.sub.2 : spring constant of base plate N/m! PA1 x.sub.1 : displacement of stage m! PA1 x.sub.2 : displacement of base plate m!, and PA1 f.sub.1 : driving force N!.
The foregoing equations can be represented, in a block diagram, by an area 3 surrounded by a broken line in FIG. 3, in which the area 3 indicates the controlled object (object to be controlled), and the part outside the area indicates a position control system block, including a position detection/conversion means 4, a compensator 5 for improving the characteristics of the position control system, a power amplifier 6, and an actuator 7. The position detection/conversion means 4 includes a stage position detector such as a laser interferometer, and a counter.
The system shown in FIG. 3 functions in the following manner. At first the position (x.sub.1 -x.sub.2) is detected, and the error(deviation) x.sub.0 -(x.sub.1 -x.sub.2) between the detected position and the target position x.sub.0 is multiplied by a positional gain k.sub.p of the position detection/conversion means 4. The obtained output drives the power amplifier 6 through the compensator 5 for improving the characteristics of the position control system. Finally a driving force f.sub.1 is generated by way of a conversion by the thrust constant k.sub.t of the actuator 7 driving the positioning device.
The feedback detection of position is represented as (x.sub.1 -x.sub.2) because the laser interferometer constituting the position detection means is usually mounted on the base plate 2. Also, in the illustrated configuration, the compensator 5 for improving the characteristics of the position control system consists of a PID compensator (P: proportional operation, I: integrating operation, D: differentiating operation). The symbols in FIG. 3 have following meanings and dimensions:
K.sub.p : positional gain V/m!, F.sub.x : P-operation gain V/V!, F.sub.i : I-operation gain V/V.multidot.sec!, F.sub.v : D-operation gain V.multidot.sec/V!, K.sub.i : driver gain A/V!, T.sub.d : time constant of driver sec!, K.sub.t : thrust constant N/A!, and s: Laplace operator rad/sec!.
For suppressing the influence of the reaction by driving the stage 1 at the position (x.sub.1 -x.sub.2), a method of detecting the acceleration of the base plate 2 and feeding back a signal, corresponding to the acceleration, to the input of the power amplifier 6 for driving the stage 1 has been disclosed in "Trial manufacture of Air Bearing Guided High Speed XY Stage", Journal of Society of Precision Engineering, 52-10, '86-10-1713.